Hyperspectral holography and spectroscopy: computational features of inverse discrete cosine transform
This work addresses computational challenges in hyperspectral imaging and spectroscopy, which are incremental improvements for applications in science and technology.
The paper tackles the problem of reconstructing spectra from diffractive intensity patterns in hyperspectral digital holography and Fourier transform spectroscopy by developing algorithms for the inverse discrete cosine transform, with proofs of perfect spectrum reconstruction and illustrations of nontrivial features.
Broadband hyperspectral digital holography and Fourier transform spectroscopy are important instruments in various science and application fields. In the digital hyperspectral holography and spectroscopy the variable of interest are obtained as inverse discrete cosine transforms of observed diffractive intensity patterns. In these notes, we provide a variety of algorithms for the inverse cosine transform with the proofs of perfect spectrum reconstruction, as well as we discuss and illustrate some nontrivial features of these algorithms.